login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A077482 Number of self-avoiding walks on square lattice trapped after n steps. 14

%I #22 Jan 05 2019 16:23:27

%S 1,2,11,25,95,228,752,1860,5741,14477,42939,109758,317147,818229,

%T 2322512,6030293,16900541,44079555,122379267,320227677,882687730,

%U 2315257359,6346076015,16675422679,45502168379,119728011251,325510252108,857400725204

%N Number of self-avoiding walks on square lattice trapped after n steps.

%C Only 1/8 of all possible walks is counted by selecting the first step in +x direction and requiring the first step changing y to be positive.

%D See references given for A001411.

%H Hugo Pfoertner, <a href="http://www.randomwalk.de/stw2d.html">Results for the 2D Self-Trapping Random Walk</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Self-AvoidingWalk.html">Self-Avoiding Walk.</a>

%e a(7) = 1 because there is only 1 self-trapping walk with 7 steps: (0,0)(1,0)(1,1)(1,2)(0,2)(-1,2)(-1,1)(0,1); a(8) = 2 because there are 2 self-trapping walks with 8 steps: (0,0)(1,0)(2,0)(2,1)(2,2)(1,2)(0,2)(0,1)(1,1) and (0,0)(1,0)(1,1)(2,1)(3,1)(3,0)(3,-1)(2,-1)(2,0).

%o FORTRAN program provided at given link.

%Y Cf. A001411, A046661, A174517, A322831.

%K more,nonn,walk

%O 7,2

%A _Hugo Pfoertner_, Nov 07 2002

%E a(26)-a(28) from _Alois P. Heinz_, Jun 16 2011

%E a(29)-a(34) from _Bert Dobbelaere_, Jan 03 2019

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)